| In NC machining, the result of the tool motion in machining a complex shape is often uncertain. Trials on actual NC machines are time consuming and costly. In principle, the material removal process can be modeled by the Boolean difference between the tool swept volume and the workpiece. One difficulty is the lack of a generalized mathematical basis for tool swept volumes. Another difficulty arises from the massive amount of data needed in the computation.;In this thesis, the formulation of swept volumes for rotational cutting tools undergoing 5-axis NC machining motions is developed. The tool swept volume is defined by its boundary which is a subset of the tool boundary during the motion. The tool boundary is represented by surfaces of revolution joined by circular edges. The tool motion is defined by the kinematics of the NC machine and the interpolation used to synchronize movements of machine axes between the initial and final positions. The Jacobian determinant in the parametric space, indicating the direction sense of the motion relative to the surface normal of the tool boundary is used to establish the necessary conditions for the boundary surfaces of tool swept volumes, which include: (1) envelopes of 1-parameter families of surfaces of revolution, (2) surfaces formed by 1-parameter families of circular edges, and (3) a subset of the initial and final instances of the tool boundary.;Massively parallel algorithms are developed and implemented on a SIMD parallel computer to: (1) generate boundary representations of tool swept volumes, (2) perform Boolean subtractions between boundary representations of the tool swept volume and the workpiece, and (3) render raster images of machined objects. A series of test cases, including four parts with spherical pockets, two propellers, and a detailed medallion, are simulated on the SIMD computer and machined on a 5-axis milling machine. In all cases, the computed models and machined parts are identical, demonstrating the correctness of the techniques.;The results of this thesis contribute to the fundamental understanding of the modeling of moving objects and machined surfaces. The use of massively parallel algorithms provides a solution to computations involving massive data and makes more accurate representations of machined surfaces feasible. This ability to generate and manipulate accurate geometric representations of tool swept volumes and machined parts is important in planning and simulating NC tool path and in the study of surface textures resulting from machining. |
